多面体曲面的离散 Yamabe 问题
Discrete Yamabe problem for polyhedral surfaces
AI总结：
本文提出多面体曲面高斯曲率的新离散化，并基于推广的离散共形等价证明每个离散共形类中存在常离散高斯曲率曲面，同时通过例子说明其一般不唯一。
摘要：
我们研究了多面体曲面高斯曲率的一种新离散化。该离散高斯曲率在多面体曲面的每个锥形奇点处定义为角亏与对应该奇点的 Voronoi 单元面积之商。我们借助 Feng Luo 开创的离散共形等价的一种推广，将多面体曲面划分为若干离散共形类。随后证明，在每个离散共形类中，都存在一个具有恒定离散高斯曲率的多面体曲面。我们还给出显式例子，以说明这种曲面通常并不唯一。
英文摘要：
We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
